jjzamball

13y = 15x

tangent = y / x  for an angle in the first quadrant, Q1.

The reference angle forms a right triangle with a base of x and a height of y.

From the equation 13y = 15x     y = 15x / 13     y/x  = 15/13    tan (theta)  = 15/13

Find the Arctan (15/13), which = tan^(-1) (15/13)    =    49 degrees to two significant digits

49 degrees  * ( pi radians / 180 degrees )   =   0.86 radians to two significant digits

  20.0185 expressed with 3 significant figures does not always mean to round to 3 figures.

If the problem is (1/3)x=9:  solve this way   3(1/3)x = 9*3       1x = 27      x = 27

If the problem is (1/3x) = 9; solve this way  3x(1/3x) = 9(3x)      1 = 27x    1/27 = 27x/27   1/27 = x

To clarify, the character for exponential is    ^

Here's an example:         22 squared is entered as "22" then "^" then "equals." The "^" character is known as a carat.

My son just learned this in this school year (11th grade).

Current educators in secondary mathematics teach students to use a method called "synthetic division."

However, following the same steps used for long division of whole numbers, a student can easily learn how to do "long division" in algebra, which includes variables, coefficients, and whole numbers.

Either can be searched online. Many students like synthetic division. I just think it is one extra technique to memorize when students already are proficient in long division of whole numbers.

This problem can be solved most easily with a calculator, but faster by regrouping. 

There are six 8's, so the problem can be rewritten as:

5 + 3 + 4 + (6 * 8) + 17 + 16 =

5 + (6 * 8) + (17 + 3) + (16 + 4) =

5 + 48 + (20 + 20) =

5 + (48 + 40) =

5 + 88 =

93

Using your algebra skills stepwise:

(x/100)*(1/3) = (5/9)

(x/100) = (5/9)*(3/1)

(x/100) = 15/9

x = (15/9)*100 

x = 1500/9 = 500/3 = 16.6666

x = 16.67 % as a percent to two decimal places

* Note: The use of 100 in the algebra was not entirely necessary, but using 100 often helps students with problems using percent notation. 

The online trig table that I cited  is in agreement with Melody.

Thanks, Melody

IF the expression should read  2 + 5 log (10000.4956) and assuming a base 10 logarithm is meant:

 2 + 5 log (10000.4956)   =  20.0001 to four decimal places.

Adding 2, the result would be 22.0001 

Pi is not infinite. It has an exact value. 

The number of decimal places that are required to express pi exactly are infinite AND never repeat.

3.1 < pi < 3.2 .... This is proof that pi is not infinite.

Phill, do you know of better advice for this ?

Look up a trig. identity for cos (a + b) by searching for "trigonometric identities.'

Then use a = 90 degrees and b = -10 degrees.

cos 90 degrees = zero, so the expression is just equal to the cos(-10 degrees).

How you should answer this problem depends on what references the you are allowed to use.

"Old school" trigonometry books had tables for all the trig function values of each individual degree.

I have such a book. I could give you the answer to four decimal places and the reference for the book.

Because of this, you might search for a "Trigonometry Table."

Provide me with the references you are allowed to use, and I will search for links to help you find a solution.

John